probability of rolling two dice and rolling a sum of 8 or a multiple of 2 on one of the dice
To find the probability of rolling a sum of 8 on two dice or rolling a multiple of 2 on one of the dice, we need to consider the possible outcomes that satisfy these conditions.
A sum of 8 can be obtained in the following ways:
- Rolling a 2 on one dice and a 6 on the other
- Rolling a 3 on one dice and a 5 on the other
- Rolling a 4 on one dice and a 4 on the other
- Rolling a 5 on one dice and a 3 on the other
- Rolling a 6 on one dice and a 2 on the other
A multiple of 2 can be obtained on either dice when rolling a 2, 4, or 6.
There are 36 possible outcomes when rolling two dice (6 possible outcomes for the first dice and 6 possible outcomes for the second dice).
Out of these 36 possible outcomes, there are 5 outcomes that result in a sum of 8 and 18 outcomes that result in a multiple of 2 on one of the dice.
To find the probability, we add the two probabilities together:
(5 outcomes + 18 outcomes) / 36 possible outcomes = 23 / 36
So the probability of rolling a sum of 8 or a multiple of 2 on one of the dice is 23/36 or approximately 0.639.